DecafDog

I'm not in Education, but I am helping my best friend look up programs like you mentioned, since she's into Educational Leadership too.
UNC chapel hill has one- https://ed.unc.edu/academics/programs/educational-leadership 
And Vanderbilt- https://peabody.vanderbilt.edu/programs/doctor-of-education-edd/
These are 2 I know from minimum research (outside of the ones you mentioned). But if I were you, I'd start here just as a jump off point to check out Education programs and then go to the schools' websites to see which ones specifically offer Educational Leadership EdDs. I believe Purdue offers Educational Leadership, but in the form of a PhD, not an EdD (https://www.education.purdue.edu/academics/graduate-students/degrees-and-programs/graduate-programs/educational-leadership/)
I'm not in the field of Education so I can't speak to the reputation of the schools, which is why I suggested US News, which seems to be an up-to-date list of good Education programs. Of course, take the list with a grain of salt in terms of measuring prestige.  
Hope this helps!

I went to SAIS straight from undergrad and chose classes based on sheer interest. Russian Economic Policy in the 90s? That sounds like fun!

Now 3 years out from grad school, I wish I had had a better understanding of the skills I needed. I could have learned Russian Economic Policy in the 90s with $1.50 in late fees at the public library - to quote Will Hunting. Not only will you get more funding, you'll also get a more beneficial education.

In hindsight, I would have taken classes in Public Finance, Public Sector Economics, Political Economy of Inequality, Mediation, Conflict Management, U.S. Constitutional Law, Policy Writing, etc. 

Historical courses are way more interesting to me, but you can learn about Belgian Independence on Wikipedia. You can't learn effective policy writing or substantive public finance knowledge on Wikipedia.

That said, if you know for sure you want to join the Federal Government, $80,000 in debt is manageable if you do income-based repayment with the Public Sector Loan Forgiveness Program - what I'm doing. If you want to do private sector, then be a lot more worried about debt since there's no way you can make that disappear in a decade other than paying them off in full.